Purpose: Fusing pre-operative and intra-operative information into a single space aims at taking advantage of two complementary modalities and necessitates a step of registration that must provide good alignment and relevant correspondences. This paper addresses both purposes in the case of 3D/2D vessel tree matching. Method: We propose a registration algorithm endorsing this vascular tree nature by providing a pairing procedure that preserves the tree topology and by integrating this pairing into an iterative algorithm maintaining pairing coherence. In addition, we define two complementary error measures quantifying the resulting alignment error and pairing error. Both are based on manual ground-truth that is independent of the type of transformation to retrieve. Results: Experiments were conducted on a database of 63 clinical cases, evaluating robustness and accuracy of our approach with respect to the iterative closest point algorithm. Conclusion: The proposed method exhibits good results both in term of pairing and alignment as well as low sensitivity to rotations to be compensated (up to 30 degrees).